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利用因子模型估计高维协方差矩阵AI 解读

High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality $p$ tends to $\infty$ as the sample size $n$ increases. Motivated by the Arbitrage Pricing Theory in finance, a multi-factor model is employed to reduce dimensionality and to estimate the covariance matrix. The factors are observable and the number of factors $K$ is allowed to grow with $p$. We…

波动率矩阵非参数估计量的聚合AI 解读

An aggregated method of nonparametric estimators based on time-domain and state-domain estimators is proposed and studied. To attenuate the curse of dimensionality, we propose a factor modeling strategy. We first investigate the asymptotic behavior of nonparametric estimators of the volatility matrix in the time domain and in the state domain. Asymptotic normality is separately established for nonparametric estimators in the time domain and state domain. These two estimators…

时间域与状态域方法的动态整合波动率估计AI 解读

Time- and state-domain methods are two common approaches for nonparametric prediction. The former predominantly uses the data in the recent history while the latter mainly relies on historical information. The question of combining these two pieces of valuable information is an interesting challenge in statistics. We surmount this problem via dynamically integrating information from both the time and the state domains. The estimators from both domains are optimally combined…